Effect of background fields on three-dimensional finite element analysis of induction logging

Three-dimensional controlled-source electromagnetic induction algorithms ar e generally formulated in terms of secondary fields or potentials. The sele ction of the primary solution is somewhat arbitrary but can greatly influen ce the efficiency of finite element codes. A simple induction logging probl em demonstrates this statement. Responses are computed using a three-dimens ional finite element method for two different selections of the primary pot ential, one that includes the borehole effect and one that does not. The ac curacy of the numerical solution, for a given mesh size, increases dramatic ally when the borehole effect is included in the primary solution. This is because the sharp gradients in the electromagnetic field near the transmitt er due to the presence of the borehole are coded as an analytic source term and do not have to be captured by the numerical approximation. Whenever po ssible, finite element analysts should select a convenient primary solution that closely matches the anticipated total solution in the immediate vicin ity of the transmitter.